Efficient computations for linear feedback control problems for target velocity matching of Navier-Stokes flows via POD and LSTM-ROM

Abstract

<p style='text-indent:20px;'>An efficient computing method for a target velocity tracking problem of fluid flows is considered. We first adopts the Lagrange multipliers method to obtain the optimality system, and then designs a simple and effective feedback control law based on the relationship between the control <inline-formula><tex-math id="M1">\begin{document}$ {{\boldsymbol f}} $\end{document}</tex-math></inline-formula> and the adjoint variable <inline-formula><tex-math id="M2">\begin{document}$ {{\boldsymbol w}} $\end{document}</tex-math></inline-formula> in the optimality system. We consider a reduced order modeling (ROM) of this problem for real-time computing. In order to improve the existing ROM method, the deep learning technique, which is currently being actively researched, is applied. We review previous research results and some computational results are presented.